The Wonky Faint
by moshpitstories
Summary: Breath-taking Quidditch can really take it out of you. As Hermione knows, life is more than just a game. General, no attributes, one-shot.


**Title:** _The Wonky Faint_

**Summary:** _Breath-taking Quidditch can really take it out of you. As Hermione knows, life is more than just a game. General, no attributes, one-shot._

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There, he could discern just a hint of flickering gold. Without even conscious thought, Harry dropped his broom into an accelerated vertical dive, straight for the Snitch he knew was almost directly beneath him. Malfoy, realizing that Harry had seen the elusive end-game piece, cried out and started diving a split-second later.

Lee Jordan, the ever-observant announcer, began a screaming narrative as the two Seekers pushed their brooms to the speed limits – Harry on his Firebolt, and Malfoy on his Nimbus 2001. Harry could see the Snitch reach a spot mere inches from the grass as they drew closer, when it started scooting erratically in an orbit just above the firm ground.

Harry held his course true, knowing he would have to pull out at the very last moment. Malfoy was hot on his tail, the greater acceleration and top speed of the Firebolt less meaningful since both of them started from almost no velocity at the same moment.

Right as his broom tip was about to brush the tip of the grass on the pitch, Harry pulled up with everything in him, his left hand automatically reaching out to grab the small flying object that ended the game. His joy at the catch was doubled at the muffled thud of Malfoy slamming into the turf as Harry successfully pulled out and flew mere inches above the ground.

Thanks to the unsurpassed extreme broom flying, Gryffindor won the game, the Quidditch Cup, and Harry Potter fell over dead.

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What?

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Right, we have all read good and bad Quidditch scenes in fanfic and canon. The reality, however, is that the very simple physics of life would kill or seriously wound anyone trying them. I have finally decided to offer a short lesson in the physics of Quidditch and broom flying, in the hopes that people will start putting a tad more reality into the situation.

Let us start with the basics. The Firebolt has an acceleration of 0-150 mph in 10 seconds, according to canon. That translates to an average acceleration of 6.71 m/s/s, which is a good bit less than gravity at roughly 9.81 m/s/s at sea level.

That means, incidentally, that you cannot take off vertically on a Firebolt – in fact, you cannot become "airborne" at all. If you lack acceleration greater than gravity, put wheels on it and call it a magic bicycle, as that is all you will get out of it. However, canon clearly demonstrates that these things fly, so there must be some other "magic" effect here. To ignore the issue completely, I will hand-wave the detail and say that the broom is similar to a wand, and uses the innate magic of the rider to generate a lift force equal to gravity. Now all that acceleration (6.71 m/s/s) can be used to fly at any angle. That means we ignore gravity on the way up, and we conveniently continue to ignore it on the way back down. Newton would be horrified, but it _is_ magic, right?

So far, so good, even if we are sweeping major problems under the "magic" label rug that appears to be bigger than Siberia.

Now, to keep the math and logic simple, assume that Harry is sitting upright on his broom – he is not tilting in any direction (forward, backward, sideways). In essence, he has a perfect seated posture and is sitting on a really thin horse. Other positions will have the same basic result, but they make the maths a tad more complex.

Right. We have our broom, we have our flyer, and we know the broom's acceleration. Frequently, authors seem to assume the Firebolt peaks at 150 mph, and they like to write about flying at "top speed" in these types of dive-for-the-ground, pull-out-at-the-last-moment, catch-the-Snitch, and listen-to-the-idiot-crash scenario that opened this discussion. Really, however, only the acceleration has been framed by canon – the top speed could be anything from 1 mph to Mach 20. In an official Quidditch pitch of 500 feet by 180 feet, travelling at 150 mph, you will completely cross the pitch long-wise in 2.27 seconds, or short-wise in 0.82 seconds. Thus long harrowing chases at top speed simply will not happen. Short harrowing chases might – if you survive them. Very, very short.

If we continue that belief, and assume a constant velocity of 150 mph (67.1 m/s), then we can determine how much g-force is exerted on the flyer by doing a particular trick. Everyone should be familiar with the concept of the g-force, as it is a common issue with pilots, astronauts, roller coasters, race car drivers, and so on.

If the broom flyer had that same perfect posture on the way down in the Wronski Feint, and pulled out at the last second, what would happen?

For our purposes, assume you have a drawing of an upright Harry sitting on a broom in a horizontal direction. During the dive, rotate the paper 90 degrees, to show the dive in perfect posture. As the catch-and-pull-out is performed, slowly rotate the paper back to the original position.

This rotation back to the original position (vertical-to-horizontal) mandates radial acceleration. Generically, a vv/r, where r is the radius of the pull-out manoeuvre in our example. Completely ignoring the "extra" effects of gravity as the flyer accelerates toward the ground, since we hold velocity as a constant, we can establish that the radial acceleration at 150 mph is roughly 4.50 kmm/s/s divided by r, the radius of the pull-out curve, where r is measured in meters.

Now, in our scenario, Harry pulled out "at the last moment" where his broom tip was about to brush the ground. Considering a typical broom is around 2m in length, and assuming the pivot point is the centre of the broom, we estimate the radius of the turn as about 1m. That means that the acceleration felt by the flyer (Harry) is approximately 4.5 km/s/s. To put that in g-force terms, divide it by the acceleration of gravity (9.81 m/s/s), and you get a comfortable result of the Seeker going through 459 g-forces.

Is that a lot?

Yeah, he is unequivocally dead. And possibly cut in half by his broom, too.

An aside is required here to discuss g-forces, and what is (and is not) possible with the human body. Did you know that astronauts are generally limited to 2-3 g-forces during take-off or landing manoeuvres? Did you know that the average human can only endure a head-to-toe g-force sensation of 3-6 without significant training? Did you know that fighter pilots can only endure 9-10 g-forces when they are physically trained and using special pressurized flight suits? Moreover, did you know that no one – trained or otherwise – can sustain more than about 3 g-forces inverted (blood rushing to the head) regardless of context?

Of course, these examples are tricky because it is less about the magnitude of the force than the duration of the force. The pressurized flight suit that some military pilots wear (many dislike the thing, as it restricts their ability to move) gives 1-2 g-forces of additional tolerance to the pilot. That means their physical training and breathing exercises get them to handling around 8 g-forces unaided. It is a long way from 8 g-forces to 459.

The human body is pretty remarkable. You can sustain a sudden g-force of up to 200, as long as it lasts in the deep-sub-second region. Such a force for even one second would (supposedly) tear your internal blood vessels to shreds. Car crashes are tricky here, because you have a sudden impact – all those g-forces are applied to a specific location behind the seat belts, and then bones break, and bad things happen. Flight in a well-padded and specially crafted seat is a different matter, distributing the pressure in a meaningful manner. But the higher the g-forces, the less amount of time you can sustain the forces exerted on the body. As little as 2 g-forces, experienced for approximately continuously for 3 seconds, is enough to cause dizziness and vision problems. When the g-forces reach 5, the same duration leads to loss-of-consciousness (LOC) unless you are physically trained _**and**_ using a pressurized flight suit. The key, however, is that acceleration means a continuing shift in pressure – unchanging values mean no g-force impacts (it becomes the relative frame of reference, much like being in an airplane, automobile, or train).

You can draw a parallel to other parts of life for what g-forces the body tolerates. Sneezing will induce 2-3 g-forces momentarily. Landing straight-legged from a short jump can induce up to 10 g-forces. These clearly fail to cause LOC or visual problems, but the reason is that the exposure time is so short. The blood shift in the body is very brief, as fluid under pressure does not just move around with brief instantaneous forces. The fluid will resist the change, thanks to inertia. Protracted exposure, or extreme magnitude for even brief moments, however, will overpower inertia and the fluid _will_ move. At low g-forces over longer periods, the fluid will pool away from the direction of travel – such as pooling in the feet, where your brain cannot use it. That deprivation leads to vision problems, dizziness, and eventual LOC – see the example of the Formula 1 race at the Texas Motor Speedway in 2001. In the instantaneous variety under very high g-forces, the fluid is moving _now_ and the blood vessels simply cannot withstand the force of movement, thereby tearing open and your internal bits turn into soup. Lovely stuff, that.

But what about being cut in half?

The typical broom is around 0.75 inches thick, but this is Quidditch, so to be generous we will allow the diameter to be in the range of 1-2 inches. Moreover, we will also assume the handle is perfectly round in cross-section, which eliminates stress concentrators that would amplify the force the broom handle would induce on the human sitting atop it. The typical adult male in moderate fitness will be approximately 8 inches through the hips front-to-back, though in a seated posture on a broom the cross-section is likely to be less linear surface in contact. However, being generous again, we will assume a full 8 inches of linear contact over the 1-2 inch diameter broom handle, even though our example is a smaller, younger male. Moreover, let us assume that a skinny teen male weighs a mere 120 lbs.

First, we need to understand how much surface area is being used by the teen. Ignoring second-order effects, we will hand-wave lots of particulars and say that the force is imparted equally across half of the surface area of the cylinder (the bottom half of the broomstick is not in supporting contact with the rider). Thus, we can say that the 8 inch cylinder with a radius of 0.5-1.0 inches comprises a surface area of 25.1-50.3 square inches, only half of which is load-bearing to the rider, so that makes it around 12.6-25.1 square inches of surface.

For a 120 lb human, that translates into about 9.55-4.77 psi (pounds per square inch) of force that the broom applies to the human. Note that this force is being applied to a rather sensitive region of the body. In comparison, using a size 11 (US) shoe on the same male, feet in properly supportive shoes comprise a surface area of about 60 square inches, for a standing-still psi of 2.00.

It is easily established that a broom rider will not be _extremely_ uncomfortable by sitting there and not doing much of anything, so long as the g-forces are set to 1. At the same time, it is not going to be comfortable, either, which is why the Cushioning Charm is incorporated. Try this at home, and you will know just how it feels. However, this entire discussion is a dissection about g-forces, and as the much longer prior analysis pointed out, moving around the pitch at high speed induces g-forces.

Essentially, at 2 g-forces, you weigh twice as much in terms of force applied to your body. So at the 459 g-forces of the dive-and-catch sequence described earlier, the rider's body is experiencing 459 times the normal weight – so from 120 lbs to a rather casual 55,080 lbs. To put that back into psi, using our _generous_ area and load estimates, the rider's pelvic region is being subjected to a measly 4,380 psi on a 1 inch diameter broom, or 2,190 psi on a 2 inch diameter broom. If I were less generous on the surface area of the broom that was load-bearing to the rider, and used a much more aggressive analysis of one-quarter of the cylinder surface area at a mere 6 inches of linear length, then the force would be a pedestrian 11,700 psi for a 1 inch diameter broom, or 5,840 psi for a 2 inch diameter broom, and those numbers are becoming closer to a "real" force load setup compared to the 4,380 psi calculation.

Is that a lot?

It depends on how you look at life, I suppose. A human can bite at 150 psi. A common, generic dog (not mastiff or pitbull or …) will bite at around 250 psi. A macaw parrot will bite at 350 psi, and that is a value that is known to snap a stout non-magical broomstick handle in half. A wolf can bite up to 1,500 psi. A very highly trained martial artist in peak physical condition can impart a kick in the range of 2,000 – 3,000 psi. (Note that such a kick will snap several ribs, break a femur, crack the skull, or the like – whatever is hit with that pressure is breaking.) The to-be-built Freedom Tower, on the site of the former World Trade Center towers, is projected to exert around 14,000 psi on the concrete base. And at the rather extreme end of "common" forces, a .357 magnum bullet impacts at around 40,000 psi. The funny thing about bones is that they tend to be a bit spring-like – slow build-up of force is much easier to handle than a sudden (very short duration) force impact. Breaking ribs requires a snap hit. If you hit-and-push, you are much less likely to break them.

At around 4,380 psi, I think everyone should agree that much pressure in such a sensitive region of the body would induce a faint. A Wonky Faint, even.

Would that flying catch of the Snitch really cut you in half?

Well, if you sustained that pressure (4,380 – 11,700 psi) for any tangible time at all (even as little as one second), yes, it likely would. If instead it lasts a very, very brief moment (perhaps a millisecond or ten), then no, you would just shatter your pelvis and any other bones in primary support positions/alignments. If you were really flying at 150 mph, the duration of your 1 meter radius pull-out would only be 0.04s. That is more than enough to be causing serious damage.

Again, this is a very simple analysis, assumes a perfect circle cross-section of the broom to eliminate stress concentrators, ignores the geometry of the human pelvis, actual load-bearing structure of the human body, and I am not doing force equations for tensile or compressive failure points based on bone density of the average human (femur strength is supposedly in the range of 1.67 108 N/m/m, knock yourself out to do the maths if you want, but remember the plasticity).

Okay, pulling off one of those spectacular dives and inducing over 400 g-forces is a bad idea. What _can_ the professional flyer do?

Extreme (read: NASCAR) car crashes can exert nearly 200 g-forces (for very, very short moments) on the occupants of the vehicle. NASCAR has quite a collection of data on this, or so I have heard through the years. It is almost certain that the military has equal if not superior data, but the odds of it being public are rather remote. The human body tends to fail fatally when receiving an abrupt full-stop impact of around 80 g-forces. If your body does not stop, but continues moving, then you are less likely to be dead – although you are still very likely to be seriously damaged. It is not the velocity that is the problem, it is the change in acceleration which causes all the problems. This is why you are fine jumping up and down on an airplane, unless it crashes – in which case, jumping up and down will not particularly cause any more damage to you than the crash itself does.

The problem with a car crash is that they tend to leave you in a lot of trouble. United States Air Force physician John Stapp is quite infamous, and worth reading about if you are unfamiliar with the name, but he demonstrated that even as little as 40 g-forces of acceleration coming to a sudden stop will snap bones, crack ribs, and eject dental fillings.

So the idea of a remotely-survivable-but-needing-immediate-medical-aid 200 g-forces acting on the human body would represent the extreme manoeuvring possible. The more mundane 40 g-forces represents a reasonable upper bound of what can be sustained as long as a full-stop impact is not the terminal outcome, if you can pardon the pun. And at 40 g-forces, the pressure exerted by the broom on the rider is in the "manageable" realm of pain, being near a human bite at maximum force. Of course, a magical broom does have that nice Cushioning Charm, which may act as a dampener of sorts to a mere one-tenth of the real force, but even magic would be hard pressed to do more than that. At 200-400 g-forces, any Cushioning Charm effect that prevents serious (shall we say, critical) injury is going to make the Enterprise engineering crew jealous, regardless of the Star Trek generation. It is far more likely to simply state that the Cushioning Charm increases the surface area of a load-bearing contact by an order of magnitude (that means 10x increase, if the term is unfamiliar to you).

Using these two framing points, we can back up and re-visit the radial acceleration. If we assume that we limit our g-forces to be in the range of 200,40, then our radius of pulling out of the constant velocity 150 mph dive is in the range of 2.29,11.5 meters. Remember, that is the radius, not the diameter. The downright pedestrian 3.5 g-forces that a rare "truly scary" rollercoaster produces would translate into a radius of a mere 131 meters. There are supposed to be around 10-20 roller coasters in the world that can induce that much in the way of g-forces. Also bear in mind that a Quidditch pitch is, in the maximum directions, 500 feet by 180 feet, or 152 meters by 54.8 meters.

So if Harry were "tearing about the pitch at top speed, searching for the Snitch", and trying to avoid LOC, then the _**radius**_ of his turn would be 131 meters. The diameter would be nearly twice the long-wise size of the pitch itself. In other words, unless he has magical binoculars on his face, he would fail to see much of anything at all, particularly with the dizziness and disorientation of a protracted 3.5 g-force flight path.

However, we have done all the work up to this point as a study of manoeuvring at the fanfic cliché top speed and constant velocity of 150 mph (again noting it could be higher or lower, all canon states is the acceleration, and that is not enough to actually achieve flight). But if you back up to the initial paragraph, the two Seekers were flying relatively slow (say, 1 m/s), looking for the Snitch, before they dropped into a dive. The second dose of reality that writers need to get is that you will not reach the "top speed" of 150 mph going from (essentially) rest toward the ground while doing a 100 – 150 ft dive.

What speed would you attain moving from rest into a maximum acceleration downward dive that lasted for 150 feet?

We will again be generous by ignoring air friction and other resisting factors. We will consider the average acceleration from the broom to be 6.71 m/s/s, as previously calculated, but we will _**ignore**_ gravity's effects. Recall that I stated previously that the broom could not, actually, fly – so to make canon work, I said that magic would counter-act one force of gravity through lift. Thus, the acceleration down is only 6.71 m/s/s, not the 16.5 m/s/s towards the ground were gravity included.

As each second elapses, the distance travelled grows with the square of time. This is elementary physics with a constant acceleration. Note that a height of 150 feet is approximately 45.7 meters. The basic distance calculation is that d equals one-half the acceleration down multiplied by elapsed time squared. So at t0, d0. At t1s, d3.35m. At t2s, d13.4m. At t3s, d30.2m, and at t4s, d53.7m or about 8 meters underground if the dive started at 150 feet elevation. The actual time to reach the target distance of 45.7 meters is a mere 3.69s.

How fast, in velocity, is the flyer going by the time 2.35s has elapsed at such an acceleration?

About 24.8 m/s, or around 55.4 mph.

Now, we can use this more limiting top flight speed for the dive, and plug it back into our earlier discussion to determine the forces that affect the rider. First, in radial acceleration, if the pull-out is at the last moment for that radius of 1m in the turn, then the rider experiences a simple 62 g-forces. In terms of pressure, this manoeuvre causes 592 psi (1 inch diameter) or 291 psi (2 inch diameter) to be imparted on the rider's pelvis – which we know is rather sensitive.

Obviously, the 1 meter radius absolute-last-moment pull-out is not going to work at this speed either. To drop the g-forces to a more realistic sudden manoeuvre of 10, it requires a turning radius of a short 6.2 meters. The same radius translates to a pressure on the groin of a rather excruciating 95.2 psi – until we remember our Cushioning Charm, which we will hand-wave at an order of magnitude reduction thanks to the increased surface area. Those 10 g-forces would be felt for around 0.39seconds. Not enough to induce LOC, but quite likely to make vision wonky.

So at a full-speed dive (in a vacuum) from 150 ft, with a turning radius of 20.3 feet the manoeuvre becomes survivable without medical aid or self-inflicted castration. It is less than pleasant, and actually attempting to catch something coming out of such a dive will be more than challenging enough, but at least remotely plausible.

Trying to catch anything other than Mr Grim Reaper out of a 459 g-force dive is simply ludicrous.

Interestingly enough, _**slower**_ brooms than the Firebolt would actually perform better at the Wronski Feint, entirely because the acceleration is less, the final velocity is less, and the sharper turning radius would result in a similar load. Flying a Firebolt at high-speed requires thinking in spherical trajectories, whilst flying an old-school broom would be more elliptical thinking which would allow more direct flight paths. There are plenty of avenues for exploration in the challenges of flying different broom types without completely ignoring the physics of the situation.

The next time you write a broom scene, take a moment to think about the forces involved. The next time you read a broom scene that is absurdly over the top, remind the author that the human body is remarkably resilient – but fails easily under pressure.

Things I spent no time discussing:

Catching a Snitch at 150 mph – whether it is stationary, flying at you, or flying from you. Try rolling down your car window at a mere 60 mph and grabbing a golf ball as you drive past. Assuming you still have intact bones in your hand, think about going more than twice as fast and doing it again. Those g-forces mean your whole body is many times its normal weight everywhere – so fine motor control in the hand, which suddenly weighs 20-200 lbs by itself, while trying to catch the Snitch . . . that is kind of like winning the lottery without purchasing a ticket.

What happens when someone ploughs into the ground at 100-150 mph? The fool following the Wronski Feint is, in essence, ready to be Wet-Dry Vac'd off the field, once they get the sticky mess into one general spot. Since in canon people _**do**_ seem to survive these little skirmishes with the frustratingly inelastic ground, it is far more likely that the top speeds are "sane" (perhaps 20 mph) during game play rather than ridiculous (90+ mph).

People that know how to drive, fly, or even ride a bike already intuitively know everything in this discussion. You already know to decelerate before taking a turn, to be careful of slip or skid conditions, to compensate for when a turning area is banked or flat, and so on. All I am trying to do is bring that intuition into play for Quidditch, with the reasons why it matters.

Left as an exercise to the reader: dealing with alternate postures of the riders, relative comparisons of brooms, imperfect broom shafts that present stress concentrators, angled dives (rather than vertical), drag forces (air is a liquid, after all), how "unbreakable" is an Unbreakable Charm, non-constant velocity and/or acceleration, and so on. You could probably do an entire thesis work studying Quidditch, the effects on humans, whether you should need a broom-flying license, and all that jive. (Cue Van Halen song here.)

_**A/N:**_

_I wrote this during lunch, doing many of the equations and such from vague recollections of undergrad – which was a long time ago. I won't claim this is entirely accurate, and welcome anyone that wants to make corrections or even use this as a starting point to launch a proper analysis. This is mostly a rant in the guise of prose, imploring people to think just a tad more. _

_This article was glanced over by one USMC pilot and (separately) by a neurologist, so while errors are mine alone, at least two people familiar with these issues deemed it sufficient (if somewhat amusing) explanation. An extra credit acknowledgement for a second pair of physics eyes to look it over and catch pesky details goes to Shev. Special thanks to those generous people – you know who you are._

_Thanks to a short list: cwarbeck, Chreechree, Sovran, and Sherylyn. _


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